What is the derivative of (ln(x+y)^2) ?

The derivative of (ln(x+y)^2) is (2ln(x+y)(1+\frac{dy)/(dx))}{x+y}

What is the first derivative of (ln(x+y)^2) ?

The first derivative of (ln(x+y)^2) is (2ln(x+y)(1+\frac{dy)/(dx))}{x+y}

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\frac{d}{d x} ((ln (x + y))^{2})

\frac{2 ln ( x + y ) ( 1 + \frac{d y}{d x} )}{x + y}

Solution steps

\frac{d}{d x} ((ln (x + y))^{2})

Apply the chain rule:

2 ln (x + y) \frac{d}{d x} (ln (x + y))

= 2 ln (x + y) \frac{d}{d x} (ln (x + y))

\frac{d}{d x} (ln (x + y)) = \frac{1 + \frac{d y}{d x}}{x + y}

= 2 ln (x + y) \frac{1 + \frac{d y}{d x}}{x + y}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 ln ( x + y ) ( 1 + \frac{d y}{d x} )}{x + y}

46240000 x^{2} - 57120 x + 17.64

(x^{2}) - 6 x - 1

x^{3} y^{3} + 8 z^{3}

2 x - x

49 a^{2} - 25 a^{2}

What is the derivative of (ln(x+y)^2) ?
The derivative of (ln(x+y)^2) is (2ln(x+y)(1+\frac{dy)/(dx))}{x+y}
What is the first derivative of (ln(x+y)^2) ?
The first derivative of (ln(x+y)^2) is (2ln(x+y)(1+\frac{dy)/(dx))}{x+y}